Add deflection in middle of edge (catenary curve)
I guess somebody has to suggest a cloth simulation, although I'm not sure it will meet your specifications. The curves resulting from pinning and tension don't appear to be catenaries, until the tension is wound up to an unrealistic level.
The topology is as shown, with the selected vertex-groups pinned in the simulation:

The edges between planes have also been given some damping in tension.. there may be more accurate settings, depending on the real-life constraints. The cloth settings are a slight variation on the 'Rubber' preset, supplied in the .blend as 'Tent', with a Shape &gt; Shrink Factor providing the forces.
The result after running the simulation for ~75 frames: